SOLUTION: The gas guage on the van initially read 1/8 full. When 15 gallons were added to the tank the guage read 3/4 full. How many more gallons are needed to fill the tank? I know the

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Question 112547: The gas guage on the van initially read 1/8 full. When 15 gallons were added to the tank the guage read 3/4 full. How many more gallons are needed to fill the tank? I know the answer is 6 but I can't get an equation to prove it.
Found 2 solutions by rapaljer, ptaylor:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = number of gallons in the tank when full.

You begin with 1/8 of the full tank, you add 15 gallons, and what you have is 3/4 of a full tank. So where x represents the "full tank", the equation is
%281%2F8%29%2Ax+%2B+15=+%283%2F4%29%2Ax+

Multiply both sides of the equation by the LCD, which is 8:
8%2A%281%2F8%29%2Ax+%2B+8%2A15=+8%2A%283%2F4%29%2Ax+
x+%2B+120=+6x+
120=5x
x=120%2F5=+24 gallons

Since you ended up with 3/4 of a tank, you have 3/4 of 24 which is 18 gallons in the car. It will take 6 gallons to fill it the rest of the way.

Pretty neat problem!!

R^2

Answer by ptaylor(2198) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=number of additional gallons needed to fill the tank
The 15 gal alone that were added filled the tank to (3/4-1/8) or 5/8 capacity. Since the tank was already 1/8 full, only 1/4 now remains to be filled. So we have the following ratio:
15 is to 5/8 as x is to 1/4 or 2/8
15/(5/8)=x/(2/8) cross multiply
15(2/8)=(5/8)x multiply both sides by 8
30=5x divide both sides by 5
x=6 gal




Hope this helps---ptaylor